By accident or by design, Jeremy Corbyn was the politician that the key European Union figures in Brussels wanted to talk about on the day the actual prime minister turned up to try to salvage her withdrawal deal.

Turning up in Brussels to try to save a deal with no specific plan, and then being advised by Donald Tusk and others to look at the "promising" plan of the opposition leader, the main feature of which (a permanent customs union) you are on record as calling a "betrayal", which is also being praised by some of your backbenchers - that probably is a special form of political purgatory.

Make no mistake, there is total fury that the PM backed the Brady amendment and undermined the deal that she told EU summits was the only one that could pass.

She sent a message to her negotiating partners that she will not "own" the domestic side of the negotiation, that the PM is now going for no-deal.

Image:Jeremy Corbyn's Brexit plan came in a letter to the prime minister

Even more than that, losing by 230 votes, having assured leaders the deal would pass, there is now a lack of trust in her credibility as a partner, her capacity to deliver the Commons.

The watchword now is "stable majority". Mrs May acknowledged this concern in a TV clip in Brussels with reference to the phrase - code in Brussels for a proper cross-party deal that can unlock EU concessions.

But the belief on the EU side is that today's Corbyn letter to the PM is a "game changer" and was mentioned to Mrs May directly by Mr Tusk and the European parliament's Brexit negotiator Guy Verhofstadt.

No Brexit breakthrough in Brussels

Mr Tusk told Mrs May that the Corbyn plan (remaining in a customs union) would be a "promising" way out of the current impasse.

This is compared to arched eyebrows at the PM talking through "various options" on the backstop rather than having a specific idea or plan to negotiate.

The Corbyn letter was seen as being drafted to push the right buttons in EU, for example by referring to "shared institutions" and now, after an attempt to win over the DUP, backing a backstop.

PM: I will deliver Brexit on time

Evidence for the lack of faith in the ability of the PM to deliver a majority was seen earlier in the week.

Top EU official Martin Selmayr turned on its head a private session of the EU Exit committee and asked Tory Brexiteer Andrea Jenkyns if she would back a deal should the EU offer a legal side deal on the backstop.

And then the PM's Chief of Staff Gavin Barwell went on a secret mission to Brussels on Monday involving meetings with senior politicos not just scoping possible concessions, but to convince them the PM has the capacity to win a stable majority.

When are the next key Brexit dates in Parliament?

The Brady amendment gambit has burnt more goodwill than it has won credibility.

All the while no-deal preparations are being ramped up, Mr Selmayr's deputy is touring EU27 capitals.

A meeting of ambassadors next week could ameliorate some of the hardest line no-deal plans, for example on aviation, a little.